Irodov question 1.7 states that:
Two swimmers leave point $A$ on one bank of the river to reach point $B$ lying right across on the other bank. One of them crosses the river along the straight line $AB$ while the other swims at right angles to the stream and then walks the distance that they have been carried away by the stream to get to point $B$. What was the velocity $u$ of their walking if both swimmers reached the destination simultaneously? The velocity of the river is $2.0$ km/h and the relative velocity of the swimmers with respect to the stream is $2.5$ km/h.
The answer in the book is $3$ km/h. However, I have got a different solution:
For the second swimmer, I have divided the time $t=t_1+t_2$ ($t_1$=swimming time, $t_2$=walking time). If we put $t=1$, then $t_1+t_2=1$. If $t=1$, then obviously the first swimmer covers a distance of $2.5$ km (I have taken the junction between the banks to be a horizontal rectangular-shape for easier calculation).
Therefore, we get, $2t_1+kt_2=2.5$. Thus, the answer will be in the series $k$(velocity)$=(2-2t)/(1-t)$. The book's answer will come if $t_1=t_2=0.5$. Is my answer correct?
The first swimmer does not cover a distance of 2.5 kilometers in one hour, because the first swimmer is fighting the current. To follow line segment $AB$, the swimmer must break up their 2.5 km/h velocity into a 2 km/h component against the current, and a component parallel to AB. The magnitude of the component parallel to AB is $\sqrt{2.5^2 - 2^2} = 1.5$. So the swimmer is traveling along AB at 1.5 km/h.
The second swimmer is not fighting the current, and so they are crossing the river at 2.5 km/h (in addition to drifting with the current at 2 km/h). So if the first swimmer reaches point $B$ at time $t$, then the width of the river is $1.5t$ km, which the second swimmer crosses in time $t_1 = \frac{1.5t}{2.5} = 0.6t$. In that time, the second swimmer has also drifted $0.6t \cdot 2 = 1.2t$ km downstream. So in the remaining time $t_2 = 0.4t$, the second swimmer must walk $1.2t$ km, which means that the walking speed must be $\frac{1.2t}{0.4t} = 3$ km/h.